Two boxes, X X\,X and YYY, contain red, blue, and green pens. Box X X\,X contains 2 red pens, 5 blue pens, and 3 green pens. Box Y Y\,Y contains 6 red pens, 2 blue pens, and 2 green pens. Casey picks one pen at random from Box X X\,X and places it into Box YYY. Casey then picks one pen at random from Box YYY.
Draw a tree diagram to represent this information.
Find the probability that Casey picks two pens of the same colour.
Given that both pens are the same colour, find the probability they are both blue.
200 exam-style questions on OCR A Level Maths 2.3 Probability, covering 2.3.1 Mutually exclusive and independent events, 2.3.2 Diagrams to assist probability calculations, 2.3.3 Conditional probability (A-level only), 2.3.4 Conditional probability from first principles (A-level only), and 2.3.5 Modelling with probability. Each one has a worked solution and a mark scheme showing where the marks go.